Cash, developer financing, gaining citizenship, using a margin loan from an investment account or a heloc on your primary in the US, seller financing, etc. are usually the best options as bank financing with attractive rates and terms usually isn't available like we're used to in the US.

If the goal is asset protection utilize bankruptcy protected assets such as retirement accounts, homesteads, private annuities, etc; an asset protection “plan” that utilizes limited partnerships, foreign asset trusts based in Nevis or the Isle of Mann, or renounce your American citizen ship and move assets to Lichtenstein.  

., people often invest in US property while living and having citizenship OVERSEAS!

if you do not have US citizenship, a green card, or a visa, make sure that if you are seeking financing that you either have a US co-sponsor or your lender can lend to foreign nationals.

I wondered if anyone has invested in Mexico- I have dual citizenship- Mexico and the US. 

A few suggestions:Get a Job, Borrow from Parents/relatives, Get a partner for the deal, or (trigger warning: not PC)  renounce US citizenship, cross the border illegally, and get all the government money you need.  

Or maybe we could grant them citizenship after they spend 5 years in the Ukrainian army?  

I do have Japanese citizenship and I’m fluent in Japanese.

The problem is that there are so many factors that impact the rate...credit score of the guarantors, Loan-to-Value, property type, citizenship status, etc...the list goes on.

Additionally, your wife's citizenship status should not impact your qualification for the exemption as long as she is a resident alien with a valid Social Security number.